MATH SOLVE

3 months ago

Q:
# In triangle MNP, angle M = 30 degrees, angle N = 20 degrees, and MN = 10 units. What is the approximate length of PN?3.8 units6.5 units15.3 units26.1 units

Accepted Solution

A:

M=30°; N=20°; MN=10 units; PN=?

In this case, we have one side MN=10 units, and the two adjacent angles, angle M=30° and angle N=20°. This is an ASA triangle (Angle Side Angle), and we can solve it using the Law of Sines:

PN / sin M=MN / sin P

PN / sin 30°=10 / sin P

angle P=?

angle M + angle N + angle P=180°

30°+20°+angle P=180°

50°+angle P=180°

Solving for angle P:

50°+angle P -50°=180°-50°

angle P=130°

Replacing in the Law of sines:

PN / sin 30°=10 / sin P

PN / sin 30°=10 / sin 130°

Solving for PN. Multiplying both sides of the equation by sin 30°:

sin 30°(PN/sin 30°)=sin 30°(10/sin 130°)

PN=10 sin 30°/sin 130°

PN=10(0.5)/0.766044443

PN=6.527036448

Rounded to one decimal place:

PN=6.5

Answer: Second option 6.5 units

In this case, we have one side MN=10 units, and the two adjacent angles, angle M=30° and angle N=20°. This is an ASA triangle (Angle Side Angle), and we can solve it using the Law of Sines:

PN / sin M=MN / sin P

PN / sin 30°=10 / sin P

angle P=?

angle M + angle N + angle P=180°

30°+20°+angle P=180°

50°+angle P=180°

Solving for angle P:

50°+angle P -50°=180°-50°

angle P=130°

Replacing in the Law of sines:

PN / sin 30°=10 / sin P

PN / sin 30°=10 / sin 130°

Solving for PN. Multiplying both sides of the equation by sin 30°:

sin 30°(PN/sin 30°)=sin 30°(10/sin 130°)

PN=10 sin 30°/sin 130°

PN=10(0.5)/0.766044443

PN=6.527036448

Rounded to one decimal place:

PN=6.5

Answer: Second option 6.5 units